Four approximate Riemann solvers from first-order up to third-order accuracy are presented and compared in this paper for solving one-dimensional rapidly varied unsteady dam-break problems with source terms over wet and dry beds. The effects of tailwater depth, channel width and channel cross-section are also explored. Simulated results are compared with analytical solution and experimental measurements to assess the performances of first-order entropy-satisfying Roe scheme, second-order TVD scheme, second-order ENO scheme, and third-order ENO scheme. For dam-break problems with source terms, the differences in accuracy of simulated results are not so significant among the four solvers. The present study integrates the four approximate Riemann solvers in a formulation together that it is convenient to obtain a suitable solution by evaluating their numerical solutions for engineers to solve different practical problems.
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Tseng et al. (2004) studied this question.